The inflationary spectrum perturbation is produced by quantum fluctuations
of fields around their homogeneous background values. The small quantum
fluctuations in the scalar field lead to fluctuations in the energy density
and in the metric, for that, we define the power spectrum of the curvature
perturbations by [1]} :
\(P_{r}(k)=\left( \frac{H^{2}}{2\pi \dot{\phi }}\right) ^{2} \) 
